A Math Forum Project

In the Dark with an Elephant - posted October 2, 2000

Please keep in mind that this is a research project, and there may sometimes be glitches with the interactive software. Please
let us know of any problems you encounter, and include the computer operating system, the browser and version you're using, and what kind of connection you have (dial-up modem, T1, cable).

Introduction

Five blind men found an elephant. Each felt the animal and described it to the others. An argument ensued.

"The elephant is like a rope," said the first man, feeling the tail.
"No, the elephant is like a wall," said the second man, feeling the side.
"The elephant is like a blanket," said the third man, feeling its ear.
"The elephant is like a tree," said the fourth man, feeling its trunk.
"You're confused. The elephant is like a spear," said the fifth man, feeling its tusk.

Then came the King. He saw the whole elephant and he alone discerned the reality of the elephant.

In this Problem of the Week, you will explore how the look of a graph of a function can vary, depending on how you set the domain and range of the graph window.

To Do and Notice:

Open the applet, below. (Note: Turn up the volume on your computer.) Experiment with changing the number values for the minimum and maximum for both the domain and range. Notice how the graph and axes look different each time after you press "Zoom." Notice that each domain and range you try is recorded in the table to the right of the graph.

Comments

Thanks for using this year's first ESCOT problem of the week!
We hope
you didn't have problems with the technology. Please let us know
if you
did.

The tricky things were getting the Views correct for question 1.
Sometimes our software didn't recognize correct solutions, but
some of
you submitted those answers anyway. We're glad you did.

View C seemed to be the hardest view, as that was the one most
often
missed. Sometimes you entered a second set of numbers for
View B. I'm
not sure why that happened.

Answers to question 2 varied, but a lot of people seemed to
understand
the concept of zooming in on a graph. Some people simply
zoomed in on
one "square" of the graph, but some people managed to stretch
out a
curve to get a straight line. Both were acceptable for the function
we
showed.

There were some interesting answers to question 3. Some of
you didn't
relate the world being flat to zooming in on a graph. The idea that
we
were looking for was that if you're very close to a curve, it will
appear flat.

A few solutions were explained very well, and they're
highlighted below. We hope you'll continue to do these
problems!

Highlighted solutions:

From:

Alex W., age 14

School:

McLean High School, McLean, VA

1. What are the values for domain and range that you found
to make the working window look like:
* View A: x min: 2, x max: 4, y min: 2, y max: 5
* View B: x min: -2, x max: 2, y min: -12, y max: 12
* View C: x min: -9, x max: -1, y min: -8, y max: 1
2. Describe a strategy to make a curve look like a line.
Look at the curve from a different point of view than ordinary, such
as from above. If you look at the curve from overhead, it looks like
a line, almost 2-D.
3. Using what you did in this PoW, explain why people might have
believed the world was flat.
People might have thought that the world was flat because their point
of view was different from a different angle. They couldn't see
everything completely.

From:

Linda M., age 13

School:

Issaquah Middle School, Issaquah, WA

1. What are the values for domain and range that you found
to make the working window look like:
* View A: X min: -5. X max: -3.5 Y min: -.7 Y max: -.1
* View B: X min: -2 X max: 2 Y min: -4 Y max: 4
* View C: X min: -5 X max: -2 Y min: -1 Y max: .7
2. Describe a strategy to make a curve look like a line.
If you zoom in really really far, a curve can look like a line.
3. Using what you did in this PoW, explain why people might have
believed the world was flat.
When you look at somthing curved very close up, it can look flat.
When you look at one little piece of the world, it looks flat, but if
you could see the whole world at one time, it would look round.

14 students received credit this week.

Erika A., age 21 - San Diego State University, San Diego, CAJacqueline B., age 20 - San Diego State University, San Diego, CAMeagan B., age 24 - San Diego State University, San Diego, CASara C., age 22 - San Diego State University, San Diego, CAAndrew H., age 12 - Caroline Davis Intermediate School, San Jose, CAKarina H., age 21 - San Diego State University, San Diego, CALynette H., age 22 - San Diego State University, San Diego, CAKyle K., age 23 - San Diego State University, San Diego, CALinda M., age 13 - Issaquah Middle School, Issaquah, WASara N., age 21 - San Diego State University, San Diego, CABhakti P., age 13 - Caroline Davis Intermediate School, San Jose, CANidia R., age 23 - San Diego State University, San Diego, CAChristine T., age 21 - San Diego State University, San Diego, CAAlex W., age 14 - McLean High School, McLean, VA